*2.4. Construction of PLES Suitability Evaluation Model on Grid Scale*

PLES suitability is to evaluate suitability in different land-utilization types of county territories with high vegetation coverage. In particular, production suitability refers to the suitability of county territories with high vegetation coverage in providing tangible agricultural products or industrial products or intangible products for humans. It mainly reflects the product production level of county territories, which is mainly affected by natural climate, land suitability, and development convenience. Living suitability refers to the suitability of county territories with high vegetation coverage in living conditions such as convenient facilities, housing, and public activities. It investigates the living support level of residents in county territories, which is mainly affected by public facilities, terrain, and the social economy. Ecological suitability refers to the suitability of the research area to provide direct or indirect ecological products and ecological services for humans, which is mainly affected by environmental quality and the social environment. The index system of PLES suitability evaluation in this paper is as follows (see Table 2):


**Table 2.** Index system of PLES suitability evaluation.


**Table 2.** *Cont.*

Note: weight of each index determined using analytic hierarchy process (AHP) and expert scoring method. The topographic position index, calculated by the slope and the elevation, was used to reflect the influence from the comprehensive geomorphic conditions of Ningbo.

#### *2.5. Coupling and Coordination Model*

The coupling coordination degree model is a relationship that can better describe the interaction and influence of two or more systems in the development process. Coupling coordination degree is the degree of mutual promotion and restriction among various systems at high and low levels and reflects the degree of interaction and coordinated development among various systems. This paper mainly adopted this model to calculate the coupling coordination degree of PLES suitability results and regional sustainable development. The coupling coordination degree (CCD) can be obtained according to the following formula. The value of CCD is in the range of 0–1. A higher value indicates a higher degree of coupling coordination [28,29].

$$D = \sqrt{\mathbb{C} \times T} \tag{1}$$

$$T = a \times l\mathbf{1}\_1 + \beta \times l\mathbf{2} + \cdots + \gamma \times l\mathbf{J} \mathbf{3} \quad \text{( $a = \beta = \gamma = 1/\mathbf{n}$ )}\tag{2}$$

$$\mathcal{C} = \sqrt[n]{(\mathcal{U}\_1 \times \mathcal{U}\_2 \times \cdots \times \mathcal{U}\_n) / \left(\frac{\mathcal{U}\_1 + \mathcal{U}\_2 + \cdots + \mathcal{U}\_n}{n}\right)^n} \tag{3}$$

$$\mathcal{U} = \sum\_{i=1}^{n} \left(\boldsymbol{\omega}\_{i} \times \mathbf{x}\_{i}\right) \tag{4}$$

where D represents the coupling and coordination degree, *T* reflects the overall effect and level of each subsystem, C is the coupling degree, U represents subsystem performance, *Wi* represents the weight value of indicator I, and *Xi* represents the standard value of indicator i in each subsystem.

There are three subsystems in this study, namely, production, life, and ecology, so C and T are calculated by the following formulas, where *Up*, *Ul*, and *Ue* are the performance levels of the PS, LS, and ES subsystems, respectively; *α*, *β*, and γ represent the contributions of the PS, ES, and LS subsystems, respectively.

$$C = \sqrt[3]{\left(\mathcal{U}\_p \times \mathcal{U}\_l \times \mathcal{U}\_c\right) / \left(\frac{\mathcal{U}\_p \times \mathcal{U}\_l \times \mathcal{U}\_c}{3}\right)^3} \tag{5}$$

$$T = \mathfrak{a} \times \mathcal{U}\_p + \beta \times \mathcal{U}\_l + \gamma \times \mathcal{U}\_c \quad (\mathfrak{a} = \beta = \gamma = 1/3) \tag{6}$$

#### *2.6. Sustainable Development Evaluation on Administration-Cell Scale*

Sustainable development is the fundamental pursuit of territorial space optimization and the starting point of PLES optimization [30]. PLES optimization is consistent with the sustainable development theory of the multi-objective coordination of economy, society,

and environment and is the embodiment and implementation of sustainable development theory in urbanization construction. On the basis of SDGs 1–3, 6, 8, 11–13, and 15, this study was guided by "intensive production", "livable life", and "beautiful ecology" to establish the coupling coordination degree evaluation index of PLES, covering the scale of space, structure of space, efficiency of space, quality of space, and other factors (Table 3). It aims to provide a scientific basis for the efficient use of PLES and the sustainable development of economy–society–environment.

**Table 3.** Index system of spatial coupling coordination degree evaluation for sustainable development goals (SDGs).


### *2.7. PLES Conflict Identification Based on Multiscale Integration Model*

In this study, the iterative method was used to establish spatial relations on different scales and perspectives [40]. According to the scores and weights of various functional evaluation factors on different scales, a multiscale mathematical model of PLES conflict weight was established:

$$\mathcal{L}\_{p,l,\epsilon} = (1 - \kappa) \times f\_{p,l,\epsilon} + a \sum\_{i=1}^{m} f\_i \times \beta\_i \tag{7}$$

where C*p,l,e* represents the comprehensive evaluation value of PLES conflict weight (p, production; l, living; e, ecological) under multiscale integration; *α* represents the weight of evaluation results at the upper scale (administrative-unit); *fp,l,e* is the evaluation index of the suitability of PLES on the grid scale; *fi* and *β* represent the evaluation factor of sustainable development of PLES on the administrative-unit scale and the corresponding index weight, respectively. Using the calculated results by the multiscale comprehensive evaluation model to diagnose the PLES conflicts of Ningbo, according to the comprehensive evaluation score of each function of each grid, the level of each function was judged. With ArcGIS, conflict types were classified on average into five levels, namely, no conflict, little conflict, medium conflict, serious conflict, and violent conflict.

## **3. Results and Analysis**
